Looking for suggestions on ways to animate images in a 3 dimensional matrix of cubes
I have the same exact questions a few years back ago. You can perhaps use Blender Modifier to achieve that, see REMESH modifier.

Actually you can do it today a lot easier using Add-On like Sverchok or Animation Nodes. 

The key answer is: VOXEL GRID. Imagine you have 3 dimensional empty point matrix, it can be in any resolution, but remember 10x10x10 is equal to 1000 and that 1000 matrix position will be replaced with geometry.

I think the most efficient way to do this is by using Particle Instancing, but you can set it up using Sverchok pretty easy.

Now for 3 dimensional empty point matrix, you either have it ON or OFF. ON means draw the Voxel. OFF means do not draw it, leave it empty. (In a more complex setup, you can have Voxel in different sizes.)

You can "fill" and draw the actual voxel box using all kind of methods. Whether using 3D Texture, or using animated deformed mesh using Armature that draw the points when it is inside (see BVHTree of Blender). 

There is no simple one answer to this. You can perhaps use Cycles Material to draw Voxel Volume Grid.